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MathsAges 16-18

Evaluating logarithms

Evaluate base-b logarithms of exact integer powers using log_b(bⁿ) = n. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  2. 2. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  3. 3. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  4. 4. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  5. 5. Evaluate log_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  6. 6. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  7. 7. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  8. 8. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  9. 9. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  10. 10. Evaluate log_4(64).

    LHS=RHS
    4 · 64 · Evaluating logarithms

  11. 11. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  12. 12. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms
12 questions · Seed 104743 · Age guidance, not curriculum certification
View the answer key
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_9(729).

    3

    Since 9^3 = 729, log_9(729) = 3.

  2. 2. Evaluate log_5(625).

    4

    Since 5^4 = 625, log_5(625) = 4.

  3. 3. Evaluate log_6(6).

    1

    Since 6^1 = 6, log_6(6) = 1.

  4. 4. Evaluate log_7(2401).

    4

    Since 7^4 = 2401, log_7(2401) = 4.

  5. 5. Evaluate log_8(64).

    2

    Since 8^2 = 64, log_8(64) = 2.

  6. 6. Evaluate log_4(256).

    4

    Since 4^4 = 256, log_4(256) = 4.

  7. 7. Evaluate log_3(81).

    4

    Since 3^4 = 81, log_3(81) = 4.

  8. 8. Evaluate log_10(10000).

    4

    Since 10^4 = 10000, log_10(10000) = 4.

  9. 9. Evaluate log_5(25).

    2

    Since 5^2 = 25, log_5(25) = 2.

  10. 10. Evaluate log_4(64).

    3

    Since 4^3 = 64, log_4(64) = 3.

  11. 11. Evaluate log_10(100).

    2

    Since 10^2 = 100, log_10(100) = 2.

  12. 12. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

12 questions · Seed 104743 · Age guidance, not curriculum certification
Worksheet StudioPractice pack · Ages 16-18

Evaluating logarithms

Take your time. Show your thinking.

  1. 1. Evaluate log_9(729).

    LHS=RHS
    9 · 729 · Evaluating logarithms

  2. 2. Evaluate log_5(625).

    LHS=RHS
    5 · 625 · Evaluating logarithms

  3. 3. Evaluate log_6(6).

    LHS=RHS
    6 · 6 · Evaluating logarithms

  4. 4. Evaluate log_7(2401).

    LHS=RHS
    7 · 2401 · Evaluating logarithms

  5. 5. Evaluate log_8(64).

    LHS=RHS
    8 · 64 · Evaluating logarithms

  6. 6. Evaluate log_4(256).

    LHS=RHS
    4 · 256 · Evaluating logarithms

  7. 7. Evaluate log_3(81).

    LHS=RHS
    3 · 81 · Evaluating logarithms

  8. 8. Evaluate log_10(10000).

    LHS=RHS
    10 · 10000 · Evaluating logarithms

  9. 9. Evaluate log_5(25).

    LHS=RHS
    5 · 25 · Evaluating logarithms

  10. 10. Evaluate log_4(64).

    LHS=RHS
    4 · 64 · Evaluating logarithms

  11. 11. Evaluate log_10(100).

    LHS=RHS
    10 · 100 · Evaluating logarithms

  12. 12. Evaluate log_8(4096).

    LHS=RHS
    8 · 4096 · Evaluating logarithms
12 questions · Seed 104743 · Age guidance, not curriculum certification
Worksheet StudioAnswer key · Ages 16-18

Evaluating logarithms

Answers and reasoning. Review before teaching.

  1. 1. Evaluate log_9(729).

    3

    Since 9^3 = 729, log_9(729) = 3.

  2. 2. Evaluate log_5(625).

    4

    Since 5^4 = 625, log_5(625) = 4.

  3. 3. Evaluate log_6(6).

    1

    Since 6^1 = 6, log_6(6) = 1.

  4. 4. Evaluate log_7(2401).

    4

    Since 7^4 = 2401, log_7(2401) = 4.

  5. 5. Evaluate log_8(64).

    2

    Since 8^2 = 64, log_8(64) = 2.

  6. 6. Evaluate log_4(256).

    4

    Since 4^4 = 256, log_4(256) = 4.

  7. 7. Evaluate log_3(81).

    4

    Since 3^4 = 81, log_3(81) = 4.

  8. 8. Evaluate log_10(10000).

    4

    Since 10^4 = 10000, log_10(10000) = 4.

  9. 9. Evaluate log_5(25).

    2

    Since 5^2 = 25, log_5(25) = 2.

  10. 10. Evaluate log_4(64).

    3

    Since 4^3 = 64, log_4(64) = 3.

  11. 11. Evaluate log_10(100).

    2

    Since 10^2 = 100, log_10(100) = 2.

  12. 12. Evaluate log_8(4096).

    4

    Since 8^4 = 4096, log_8(4096) = 4.

12 questions · Seed 104743 · Age guidance, not curriculum certification